Low-lying spin excitations due to next-nearest neighbour interactions in a ferromagnetic lattice with a body-centred cubic (bcc) crystal structure

Spin excitations due to the next-nearest-neighbour interactions are investigated for a ferromagnetic lattice with a body-centred cubic (bcc) crystal structure. Using the three-dimensional Heisenberg spin model in a uniform external magnetic field, both the nearest-neighbour (NN) and next-nearest-neighbour (NNN) exchange interactions are considered. The spin wave energies at low temperatures are calculated for which the system is close to its ground state. From the dispersion plots, the additional exchange interactions by the NNN cause an increase in the spin excitation energies.